Question: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $y \neq 0$. $p = \dfrac{5}{4(y + 9)} \div \dfrac{8y}{4y(y + 9)} $
Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{5}{4(y + 9)} \times \dfrac{4y(y + 9)}{8y} $ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 5 \times 4y(y + 9) } { 4(y + 9) \times 8y } $ $ p = \dfrac{20y(y + 9)}{32y(y + 9)} $ We can cancel the $y + 9$ so long as $y + 9 \neq 0$ Therefore $y \neq -9$ $p = \dfrac{20y \cancel{(y + 9})}{32y \cancel{(y + 9)}} = \dfrac{20y}{32y} = \dfrac{5}{8} $